Question

A tridiagonal matrix is a square matrix with zeroes everywhere except on the main diagonal and the diagonals just above and below the main diagonal.

Let \(T\) be a real anti-symmetric tridiagonal matrix with elements \(t_{12}=c_{1}, t_{23}=c_{2}, \ldots\), \(t_{n-1 n}=c_{n-1}\). If \(n\) is even, compute det \(T\).